Internal problem ID [2564]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }-y \left (x^{2}+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve((x^2-1)*diff(y(x),x)=(x^2+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x} \left (x -1\right ) c_{1}}{x +1} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 25
DSolve[(x^2-1)*y'[x]==(x^2+1)*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {c_1 e^x (x-1)}{x+1} \\ y(x)\to 0 \\ \end{align*}